This concept is usually drawn from Matthew 24:34, “I tell you the truth, this generation will certainly not pass away until all these things have happened.” The previous verses, Matthew 24:1-33, describe end-times events in relation to Israel. As a result, some interpreters thought that the end times would begin when Israel was “reconstituted” as a nation (which happened in 1948). However, as more and more time passed from 1948, the time span of a “generation” began to lengthen and lengthen. It has now been more than 60 years – which is far beyond any standard definition of a generation.
The biggest problem with this teaching is that it completely misunderstands Matthew 24:34. What the context appears to say is that once the end-times events begin to happen, they will happen quickly. Further, Jesus' prophetic words in Matthew 24 seem to have a "double fulfillment." Some of the events occurred in A.D. 70 when the Romans destroyed Jerusalem and Israel. Other events (24:29-31, for example) have clearly not yet occurred. Some of Jesus' words occurred shortly after He spoke them (this generation will not pass); others have not yet occurred. To answer your question directly, no, it is not scriptural to teach that the generation that sees Israel become a nation will also see the second coming of Jesus Christ. This may be the case, but Scripture does not specifically say so.